Binary, Octa and Hexa Conversion

There are infinite ways to represent a number. The four commonly associated with modern computers and digital electronics are: decimal, binary, octal, and hexadecimal.

Decimal (base 10) is the way most human beings represent numbers. Decimal is sometimes abbreviated as dec.

Decimal counting goes:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and so on.

Binary (base 2) is the natural way most digital circuits represent and manipulate numbers. Binary numbers are sometimes represented by preceding the value with '0b', as in 0b1011. Binary is sometimes abbreviated as bin.

0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, and so on.

Octal (base 8):- Octal is sometimes abbreviated as oct.

Octal counting goes: 0 to 7 and its combination
0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, and so on.

Hexadecimal (base 16)

Hexadecimal counting goes: 0 to 9 and A to F and its combination (E=10 and F=15)
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, and so on.

Converting Binary to Octal:-

Group Binary digit into group of three( should be 7) from right.(add 0 to left side if group of 3 digit is not possible )

10011011= 010 011 011 = 0²+2¹+0⁰  0²+2¹+2⁰ 0²+2¹+2⁰ =  233

10101 = 010 101 = 0+2+0 4+0+1 = 25

Binary to Hexadecimal:-

Group Binary digit into group of 4 from right to left

10101 = 0001 0101 = 0+0+0+1 0+4+0+1=15 (if first group itself was 15 then it will be F but 15 is the combination of two groups)

Converting Octal to Binary:-

345 = find the binary of each digit and combine them.

Converting Hexadecimal to Binary:

Hexadecimal Number : 15₁₆

1 in binary is 1

5 in binary in group of 4 is = 0101

Combine them = 10101

Converting Binary to Decimal:-

1010 = 2³+0²+1¹+0⁰ =8+2 =10

Decimal, binary, octal and hexadecimal of 0 and 1 are 0 and 1 itself.

while converting binary to octa or hexa, group them in 3 or 4 respectively combine each group(but add digits within group)